update formats and lecture notes

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Trance-0
2025-10-31 11:52:02 -05:00
parent 9a9ca265ec
commit f13b49aa92
7 changed files with 154 additions and 20 deletions

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@@ -145,7 +145,8 @@ Since $b$ is fixed, so this is in 1-1 correspondence with $A$, so it's countable
Let $A$ be the set of all sequences for 0s and 1s. Then $A$ is uncountable.
Proof:
<details>
<summary>Proof</summary>
Let $E\subset A$ be a countable subset. We'll show $A\backslash E\neq \phi$ (i.e.$\exists t\in A$ such that $t\notin E$)
@@ -155,4 +156,4 @@ Then we define a new sequence $t$ which differs from $S_1$'s first bit and $S_2$
This is called Cantor's diagonal argument.
QED
</details>